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Sparse binary matrices are of great interest in the field of compressed sensing. This class of matrices make possible to perform signal recovery with lower storage costs and faster decoding algorithms. In particular, random matrices formed by i.i.d Bernoulli p random variables are of practical relevance in the context of nonnegative sparse recovery. In this work, we investigate the robust nullspace property of sparse Bernoulli p matrices. Previous results in the literature establish that sucharXiv:2112.14148v2 fatcat:l62pyces45hybm3wfvwfnbg6iy